Applied algebra, algebraic algorithms and error-correcting - download pdf or read online

By Serdar Boztas, Hsiao-feng Lu

ISBN-10: 3540772235

ISBN-13: 9783540772231

This publication constitutes the refereed lawsuits of the seventeenth foreign Symposium on utilized Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-17, held in Bangalore, India, in December 2007.

The 33 revised complete papers provided including eight invited papers have been conscientiously reviewed and chosen from sixty one submissions. one of the topics addressed are block codes, together with list-decoding algorithms; algebra and codes: jewelry, fields, algebraic geometry codes; algebra: jewelry and fields, polynomials, variations, lattices; cryptography: cryptanalysis and complexity; computational algebra: algebraic algorithms and transforms; sequences and boolean functions.

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Extra resources for Applied algebra, algebraic algorithms and error-correcting codes: 17th international symposium, AAECC-17, Bangalore, India, December 16-20, 2007: proceedings

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To conclude we summarize the current situation: Edwards coordinates offer the only complete addition law stated in the literature. If completeness is not required then inverted Edwards coordinates are the new speed leader. References 1. , Lange, T. ): INDOCRYPT 2006. LNCS, vol. 4329. Springer, Heidelberg (2006) 2. : Optimizing Double-Base Elliptic-Curve Single-Scalar Multiplication. , Yung, M. ) INDOCRYPT 2007. LNCS, vol. 4859, pp. 167–182. Springer, Heidelberg (2007) 3. org/EFD 4. : Faster Addition and Doubling on Elliptic Curves.

To derive these output rules, observe that two points (x1 , y1 ) and (x2 , y2 ) on the Edwards curve have sum (0, 1) if and only if (x2 , y2 ) = (−x1 , y1 ). In this case (Z2 /X2 , Z2 /Y2 ) = (−Z1 /X1 , Z1 /Y1 ) so, in the notation of our explicit formulas, I = X1 Y2 + Y1 X2 = X1 Y1 Z2 /Z1 − Y1 X1 Z2 /Z1 = 0 and Y2 Z1 = Y1 Z2 . Similarly, two points (x1 , y1 ) and (x2 , y2 ) having sum (0, −1) end up with I = 0 but with Y2 Z1 = −Y1 Z2 ; two points (x1 , y1 ) and (x2 , y2 ) having sum (1, 0) end up with H = 0 and Y2 Z1 = X1 Z2 ; two points (x1 , y1 ) and (x2 , y2 ) having sum (−1, 0) end up with H = 0 but with Y2 Z1 = −X1 Z2 .

Gold and Kasami-Welch Functions, Quadratic Forms, and Bent Functions. In: Advances in Mathematics of Communications (2007) 9. : Nonsingular Bilinear Maps, Spaces of Matrices, Immersions and Embeddings. edu Abstract. Under the notion of list decoding, the decoder is allowed to output a small list of codeword such that the transmitted codeword is present in the list. Even though combinatorial limitations on list decoding had been known since the 1970’s, there was essentially no algorithmic progress till the breakthrough works of Sudan [14] and GuruswamiSudan [11] in the mid to late 1990’s.

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Applied algebra, algebraic algorithms and error-correcting codes: 17th international symposium, AAECC-17, Bangalore, India, December 16-20, 2007: proceedings by Serdar Boztas, Hsiao-feng Lu


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